How can I assign shortcuts to "Auto Execution" and "Always" checkbox of animation nodes in node editor toolbar?
As far as I know, one can't set a shortcut to toggle a checkbox. The only way to do that is to create an addon that register an operator that does the toggle and create a custom keymap for your shortcut as described here. 

Animation Nodes define the key combination Ctrl + Shift + Q to disable Auto Execution as described in the documentation.